Welcome! Lesson details for each day are described below. I will do my best to not only stay updated, but also provide extra links and resources for you to use and explore. My Channel for Precalculus
Helpful Tutor: Drew Laiche (www.mrLaiche.com). Advanced Math Tutor. firstname.lastname@example.org
Unit 3: Exponential and Logarithmic Functions
Day 27: November 16th: Objective: Students will review the assignment from last class working through the homework questions together. Today’s in class notes: PC3-3SelectedAnswers I picked what I thought was the best example of the homework and scanned those problems. Make sure to e-mail me other questions as they come up. Homework: Finish the homework from last class if you didn’t already (it’s listed right below). Also preview the next lesson by reading pages 350-357. Take notes by writing down the theorems and formulas you see. When a formula or theorem is shown, make sure to define any variables that occur in the formula. For example, the Simple Interest Formula on page 350 defines I=Prt. You should have a sentence or two about what this formula does, as well as an explanation of what I, P, r, and t all stand for.
Day 26: November 14th. Objective: Students will use properties of logarithms to solve equations.Notes: PC3-3PartANotesKey and PC3-3PartBNotesKey Homework: PC 3-3(part1) worksheet #’s 13, 14, 15, 16, 23, 24, 27, 29, 30, 43, 44. ALSO: PC 3-3(part 2) worksheet ALL 8 problems.
Day 25: November 7th. Objective: Students will find the domain of a logarithm. Students will complete application problems with exponential and logarithmic functions. Notes: PC3-2Notes Class work: PC3-2Assignment Homework: p. 330 #’s 37-45 odd, #’s 77-82 ALL. Preview the properties of logarithms for the next lesson!
Day 24: November 2nd. Objective: Students will graph the exponential and logarithmic functions. Students will convert between exponential and logarithmic functions. Notes: PC3-1Notes:Assignment Notes Key: PC3-1NotesKey Homework: p 320 #’s 39,40,41, and 61. p. 330 #’s 1-29 odd.
Unit 2: Polynomial and Rational Functions
Day 23: October 31st. Objective: Students will prove their knowledge by completing a chapter test. Homework: Preview the next unit on exponential functions and logarithms. Answer the question: What is the circle of logs?
Day 21: October 27th. Objective: Students will collaborate in order to complete a group test. Homework: Study for the individual test on Tuesday! Helpful Study Resource: Take a look at all of your quizzes from this unit. We’ve covered quite a bit. I’m linking the answer key’s right here: PC2-QuizzesKey Also, there are other review problems in your book at the end of the chapter. Group Test (Blank): PC2-GroupTestPart1and2
Day 20: October 25th. Objective: Students will write equations of rational functions given a graph. PC2-6 Homework: Study for the group test on Friday!
Day 19: October 23rd. Objective: Students will identify horizontal and oblique asymptotes in a rational function. Notes: PC2-5Notes Notes Key: PC2-5NotesKey Assignment: PC2-5PracticeProblems Homework: Finish all practice problems (in your notebook). PC2-5PracticeProblems
Day 18: October 19th. Objective: Students will determine the x-intercepts, y-intercept, domain, and vertical asymptotes of a rational function. Notes: PC2-4Notes Notes Key: PC2-4NotesKey Assignment (Homework): PC2-4Assignment.
Day 17: October 17th. Objective: Students will determine the number of positive, negative, and imaginary roots using Descartes Rule of Signs. Students will use the Rational Zeros Theorem to create a list of potential rational zeros of a function. Notes: PC2-3Notes Homework: p. 263 #’s 1,2,3. p. 264 #’s 11-15 odd, 41-49 odd.
Day 16: October 12th. Objective: Students will simplify expressions necessary for writing solutions for polynomials. Peer-Graded Quiz: PC2-2Quiz Practice Problems: PC2-SkillBuilding Key: PC2-SkillbuildingKey Homework: p 273 #’s 45-53 odd, p. 279 #’s 1-9 odd. Also, watch these two videos: Descartes Rule of Signs and Rational Roots Theorem. Write down one question for each video. The questions will be required for a stamp.
Day 15: October 10th. Objective: Students will write the equation of a polynomial given its roots. Students will identify the roots of a polynomial. Intro Notes: PC2-2(Pre)Notes Key: PC2-2PreKey “Real” Notes: PC2-2Notes Key: PC2-2NotesKey(1) and PC2-2NotesKey(2) Homework: PC2-2 (complete them all).
Day 14: October 6th. Objective: Students will analyze polynomials including power functions. Class work: PC2-0 Notes: PC2-1 Answer Keys: PC2-0FrontKey , PC2-0BackKey , PC2-1FrontKey and PC2-1BackKey Homework: p 214 #’s 1-6 ALL. p 224 #’s 1-19 odd. Interesting Link regarding where you study: Economist
Unit 1: Functions and Their Graphs
Day 13: October 4th. Objective: Students will prove their knowledge by completing a test. Homework: none.
Day 12: October 2nd. Objective: Students will review the difference quotient, transformations, compositions, and inverses to prepare for a test. Review: PC1-Review(2) Homework: Study for the test on Wednesday! Review ANSWER KEY: PC1-Review(2)KEY
Day 11: September 28th. Objective: Students will find the inverse of functions if they exist. Notes: PC1-9Notes Completed Notes: PC1-9CompletedNotes Homework: p 308 #’s 21-29 odd (Verify they are inverses of each other) #’s 47-53 odd (Find the inverse) Homework Help: Here is a scan of finding the inverse step-by-step: InvserseStepbyStep
Day 10: September 26th. Objective: Students will explore compositions of functions algebraically, graphically, and in a table. Notes: PC1-8Notes Completed Notes: PC1-8NotesCompleted Practice Problems: PC1-8Practice Homework: p. 170 #’s 1-11 odd. #’s 31-39 odd.
Day 9: September 22nd. Objective: Students will perform transformations of functions including reflections, stretches, and shifts. Notes: PC1-7Notes Completed Notes: PC1-7A Completed and PC1-7B Completed Practice Problems (Homework): PC1-7PracticeProblems Helpful videos are linked below in my previous post. I did explain it differently in class, but it’s the same concept.
Day 8: September 20th. Objective: Students will evaluate the difference quotient given a function. Students will translate functions up,down,left, and right. Notes and Problems: PC1-5NotesandProblems Glue In: PC 1-5 Glue In Complete Glue In: PC1-5NotesScan Class Assignment: PC1-6Exploration Homework: p 150 #’s 81-84 all (Just evaluate the difference quotient for each of them). p. 162 #’s 1-24 all (Make sure to sketch the graph and write the equation for all of them). Helpful Video #1: Transformations 1 Helpful Video #2: Transformations 2 Helpful Video #3: Transformations 3 Helpful Video #4: Transformations 4
Day 7: September 18th. Objective: Students will prove their knowledge by completing a unit test.
Day 6: September 14th. Objective: Students will summarize concepts and review for a chapter test. Review: PC1-Review Review Answer Key: PC1ReviewKey Homework: Complete the review, check your answers, and study for the test next class.
Day 5: September 12th. Objective: Students will determine if a function is even, odd, or neither both algebraically and graphically. Glue In Notes: PC1-4 Notes Completed Glue In Notes: PC1-4CompleteNotes IN Class Assignment KEY: PC1-4PracticeProblemsKey Group Practice Quiz: PC1-GroupPracticeQuiz Group Quiz Key: PC1GroupQuizKey Homework: p. 148 #’s 9-23 odd (Part c only) #’s 41-53 odd (Determine even/odd/neither algebraically).
Day 4: September 8th. Objective: Students will identify intervals for when a function is concave up and concave down. Students will identify local minima and maxima as well as absolute minimum and maximum. Notes: PC1-3Notes (Completed Notes From Class Homework: p. 151 #’s 85-88 ALL #’s 95 – 101 Graph with assistance from a device, find the Intervals Increasing/Decreasing, Local Max/Min, as well as find the intervals the graph is concave up/down. Also: #103 (TOTAL PROBLEMS – 13). Video on Increasing/Decreasing and Concavity: YouTube. Video on problem #103: YouTube
Day 3: September 6th. Objective: Students will identify intervals for when a function is increasing and decreasing including problems involving piecewise functions. Notes: PC1-2Notes Homework: p. 148 #1-8 all, 9-25 odd NOT (c).
Day 2: September 1st. Objective: Students will find the domain of a function algebraically and graphically. Students will find the range of a function graphically. Notes: PC1-1Notes (updated). Assignment/Homework: p. 125 #’s 1-13 odd, #’s 21-63 odd. Show work (including drawing graphs). Use these scans to do homework if you don’t have a book yet. 2.1-prob.-set-page-1 and 2.1-prob.-set-page-2. Helpful Video: Domain and Range (Basic).
Day 1: August 30th. Objective: Students will read syllabus, understand course expectations, and pre-assess unit 1 material. Syllabus: Syllabus Worksheet/Homework: Day 1 what do you know. Helpful Notes from Class: PC1-0 Notes Scan Supplemental Links: Is it a function? or What is a function?